Toilet not flushing properly

[sarahh96]

Apologies in advance for this mind numbing problem. I'm just wondering if anyone's found a solution to this.
We have a 20 yr old toilet which had the old ball cock system in it.
About 3 yrs ago we had to have that replaced and they put in a new type ballcock thing.
Anyway, ever since then it hasnt flushed properly. It's takes human stuff away but always leaves the paper floating around. Takes a double flush to get the paper down.
I've asked a plumber, he doesn't know the answer.
I've plunged, used one of those drain snake things, poured viakal down it and still the bloody thing won't clear in one.
Anyone else had this problem?
I'm beginning to think it's maybe something to do with the paper ie: recycled so maybe more buoyant? I'm tempted to get some drain unblocker down there but not sure if it'll do damage to the pipe work.
Plumber did mention that new cisterns hold less capacity water as a water saving thing and that can be the cause but we still have a large capacity cistern.
Anyway, I'm boring myself with this now so if you've got this far and are still reading, well done!
Any advice?

Is it a dual flush one that you can press and hold down for extra oomph?

Modern flushes are rubbish, I find. Using only 2ply rather than 3ply paper helps a bit.

I long for one of those Victorian type high up cisterns!

Watching with interest as have same problem exactly. Old flush handle so no double pushing to help. Most inefficient flush!

This.

I wouldn't bother with drain unblocker, btw. Fairy liquid and a couple of buckets of warm water is good at shifting any blockages.

No duel flush, old school handle I'm afraid. Interesting about the ply though. Interesting that it's not just me with the problem!